The reachable set estimation for linear systems subject to both discrete and distributed delays is considered in this study. By choosing appropriate Lyapunov–Krasovkii functionals, some sufficient conditions are established to guarantee that all the states starting from the origin are bounded by an ellipsoid. The problem of finding the smallest possible ellipsoid can be transformed into an optimisation problem with matrix inequality constraints. Moreover, the computational complexity is reduced since fewer variables are involved in the obtained results. These criteria are further extended to systems with polytopic uncertainties. It is shown that in the absence of distributed delay, the obtained condition is also less conservative than the existing ones.

This study presents the implementation of a hybrid control strategy that is applied to a brushless AC (BLAC) motor drive. Hybrid control is a general approach for control of switching-based hybrid systems (HS). This class of HS includes a continuous process, controlled by a discrete controller with a finite number of states. The overall stability of the system is shown with the use of Lyapunov technique. The Lyapunov functions contain a term that penalises incremental energy of control error, torque and stator current, which enhances the stability. The closed-loop system, with the proposed control law, provides good transient response and good regulation of the BLAC motor control. A new logical field programmable gate array current (torque) controller is developed, based on the Lyapunov theory. The reference tracking performance of speed and torque (current) is demonstrated in terms of transient characteristics through simulation and experimental results.

This study investigates the problem of state feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems (SPSs) with parameter uncertainty. The considered system is approximated by Takagi–Sugeno fuzzy model. Based on a matrix spectral norm approach, new sufficient conditions, which ensure the existence of state feedback controller such that the resulting closed-loop system is asymptotically stable, are given. The gains of controllers are obtained by solving a set of ɛ-independent linear matrix inequalities (LMIs) such that, the ill-conditioned problems caused by ɛ can be easily avoided. In contrast to the existing results, the proposed method can be applied to both certain and uncertain SPSs with greater singular perturbation parameter ɛ. A numerical example is provided to illustrate the reduced conservatism of the authors’ results.

The authors investigate in this study the problem of designing decentralised quantised ℋ_∞ feedback control for a class of linear interconnected discrete-time systems. The system has unknown-but-bounded couplings and interval delays. The quantiser has an arbitrary form that satisfies a quadratic inequality constraint. A linear matrix inequality (LMI)-based method using a decentralised quantised output-feedback controller is designed at the subsystem level to render the closed-loop system delay dependent asymptotically stable with guaranteed γ-level. To show the generality of the authors' approach, it is established that several cases of interest are readily derived as special cases. The authors illustrate the theoretical developments by numerical simulations.

In this study, a methodology to compute achievable performance bounds for non-right-invertible, stable, discrete-time MIMO systems is proposed. This methodology is based on the definition of a new performance index, which is the cumulative, squared and exponentially weighted tracking error to a step reference. The results include expressions for the optimal value of this performance index and for the Youla parameter that is able to achieve such performance. For a particular class of single-input multiple-output plants, closed-form expressions depending on the dynamic features of the plant are also obtained. A discussion on the selection of the speed of decay of the exponential weight and its influence on optimal closed-loop stability is included. Numerical examples are presented to illustrate the results.

A digital signal processor-based cross-coupled functional link (FL) radial basis function network (FLRBFN) control is proposed in this study for the synchronous control of a dual linear motors servo system that is installed in a gantry position stage. The dual linear motors servo system comprises two parallel permanent magnet linear synchronous motors (PMLSMs). First, the dynamics of the field-oriented control PMLSM servo drive with a lumped uncertainty, which contains parameter variations, external disturbance and friction force, is introduced. Then, to achieve accurate trajectory tracking performance with robustness, an intelligent control approach using FLRBFN is proposed for the field-oriented control PMLSM servo drive system. The proposed FLRBFN is a radial basis function network embedded with a FL neural network. Moreover, to guarantee the convergence of the FLRBFN, a discrete-type Lyapunov function is provided to determine the varied learning rates of the FLRBFN. In addition, since a cross-coupled technology is incorporated into the proposed intelligent control scheme for the gantry position stage, both the position tracking errors and synchronous errors of dual linear motors will converge to zero, simultaneously. Finally, some experimental results are illustrated to depict the validity of the proposed control approach.

The problem on the existence of a common quadratic Lyapunov function (CQLF) for discrete switched linear systems with m stable subsystems is considered. System matrices are Schur stable. A necessary condition for the existence of a CQLF and a sufficient condition for the non-existence of a CQLF are derived, respectively. Numerical examples are presented to illustrate the results.

The authors investigate a class of observer-based discrete-time networked control systems (NCSs) with multiple-packet transmission where random packet dropouts occur independently in both the sensor-to-controller (S/C) and controller-to-actuator (C/A) channels. The authors first propose and prove the separation principle for the NCSs where packet dropouts in the C/A and S/C channels are governed by two independent Markov chains, respectively. Secondly, the authors derive a sufficient condition, in terms of linear matrix inequalities (LMIs), for stabilisation control of the Markov chain-driven NCSs. The authors also derive the necessary and sufficient condition for stabilisation control of the memoryless process-driven NCSs as a special case. A numerical example is provided to illustrate the effectiveness of our method.

In this study, the robust stochastic stability problem for discrete-time uncertain singular Markov jump systems with actuator saturation is considered. A sufficient condition that guarantees that the discrete-time singular Markov jump systems with actuator saturation is regular, causal and stochastically stable is established. With this condition, for full and partial knowledge of transition probabilities cases, the design of robust state feedback controller is developed based on linear matrix inequality (LMI) approach. A numerical example is given to illustrate the effectiveness of the proposed methods.

Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.

A new memory-reliable controller design for a class of discrete-time systems with time-varying input delays is proposed. By assuming that the actuator fault obeys a certain probabilistic distribution, a new practical actuator fault model is presented. Based on this fault model and the known past information, an augmented system with time-varying delay or non-delay, similar to switched systems, is established. By using the Lyapunov–Krasovskii approach, a sufficient condition for the existence of reliable controller is expressed by linear matrix inequalities. An illustrative example is exploited to show the effectiveness of the proposed design procedures.